# Is Newton's third law really correct? [closed]

Suppose I am pushing a box on table with $$10$$ N force due to friction it is not moving and if i applied $$20$$ N the box started accelerating. Then, how does the box apply $$20$$ N force on me?Well actually,I really know fundamental laws are certainly true.But from where the opposing force on us is coming?

## closed as unclear what you're asking by Feynmans Out for Grumpy Cat, David Z♦Jun 17 at 8:50

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• I am voting to close this question as it is unclear what you are asking. – Feynmans Out for Grumpy Cat Jun 16 at 22:13
• You may want to change your title as it does not adequately describe your question. – my2cts Jun 16 at 23:15
• Here's a suggestion - any time you want to ask a question such as "Is (some basic and fundamental law of nature) really correct?", take my advice and answer, "Yes - it's my understanding that's faulty", and then go study until you understand what the law is and why you misunderstood it. This will save you immense amounts of time... – Bob Jarvis Jun 17 at 2:52
• @BobJarvis However, I think it is perfectly fine to ask questions (on PSE) relating to the mismatch between one's understanding of the law and the actual law. Of course, in this particular post, it is just unclear to understand what the OP is trying to ask. – Feynmans Out for Grumpy Cat Jun 17 at 11:38
• @FeynmansOutforGrumpyCat - yes, absolutely - but that wasn't the question which was asked. The question "Is Newton's third law really correct?" implies that OP believes the Newton's third law is actually not correct, and everyone is just playing silly buggers with him. – Bob Jarvis Jun 17 at 11:51

The difficulty you are having is quite common when first learning Newtons laws because you think Newton’s third law means the forces always cancel each other and nothing should accelerate. They don’t. You have to look at the net force acting on each body individually and apply Newton's second law to each individually.

When you were pushing on the box, say to the right, with a force of 10 N, an equal static friction force of 10 N was acting on the box to the left in opposition to your force. The net force on the box was zero and therefore it did not accelerate.

Per Newton's third law the box was exerting an equal and opposite force of 10 N on you to the left. You did not accelerate because of an equal and opposite static friction force between your feet and the ground that acted to the right. Therefore you do not accelerate.

Now when you were pushing with a 20 N force to the right the box accelerated because your force apparently exceeded the maximum static friction force between the box and ground acting to the left. The box is now sliding and it is the kinetic friction force, which is generally less than the static friction force, between the box and the ground that is now opposing your force. But since the box is accelerating your 20 N force to the right was greater than the kinetic friction force to the left, meaning there was a net force to the right, $$F_{net}$$, causing the box to accelerate per Newton's second law. Then, per Newton's second, the acceleration of the box to the right is $$a=\frac{F_{net}}{m}$$, where $$m$$ is the mass of the box.

Now the box also exerts an equal and opposite 20 N force on you per Newton's third law. What keeps you from accelerating? It is the static friction force between your feet and the ground acting to the right that is equal to the force the box exerts on you. The net force on you is zero as long as you don't push too hard that the maximum static friction force between your feet and the ground is exceeded, in which case you will start slipping.

Hope this helps.

• This also points to boxes that you can't push, because their max static friction exceeds your own. – Caleth Jun 17 at 8:25
• It could help to imagine you standing on a treadmill, while the box is standing on a solid table. When you push the box, you will push yourself back on the treadmill and will have to keep taking steps to walk forward to keep pushing the box. The force that is moving the treadmill is the force of the box, which is pushing back on your hands, through your body onto the treadmill. – Falco Jun 17 at 8:40
1. Imagine that you have springs instead of your hands. If you push the box, the springs are compressed, shortened by the force from the box. (No box, no compress as you move.)

2. The side of box on which you push is slightly deformed - imagine that it is from very springy material, so you can see it. As you deform it more and more, it acts to you with greater and greater force - similarly as a drawn bow.

3. You may stop pushing the box when it starts accelerating - but the box immediately stops accelerating. To keep it in the accelerated motion, you have to keep pushing on it - and then the box will keep pushing on your hands - see 1. and 2.

Suppose the box is half your mass and you stand on a skateboard, and just think of the second part of your experiment. If you think that pushing the box will also make you move backward, then you agree (at least qualitatively) with Newton's third law. :)

I’d like to note here that there is an intuition that might lead one astray here: when you’re actually pushing on a static object that is stuck to the ground due to friction, it usually becomes easier to push it immediately after it slips. This is because the coefficient of static friction tends to be greater than that of kinetic friction.

So if you’re actually pushing a big heavy box along the floor and you find it becomes easier when it starts to slip, this isn’t because Newton’s third law is incorrect, but because you can continue pushing the moving box with a force that is less than that which you had to exert to start moving the box. E.g., if the box is 50kg and the coefficient of status friction is .8 while the coefficient of kinetic friction is .4, then you may find that it takes

$$F = \mu_s m g \sim 400 N$$

to get the box moving, but then once you do you can relax and push with only a force of

$$F = \mu_k m g \sim 200 N$$

to keep the box moving at constant speed. So it gets easier, and there is no contradiction with Newton’s Third.